Central Forces 2021
Consider the normalized wavefunction \(\Phi\left(\phi\right)\) for a
quantum mechanical particle of mass \(\mu\) constrained to move on a
circle of radius \(r_0\), given by:
\begin{equation}
\Phi\left(\phi\right)= \frac{N}{2+\cos(3\phi)}
\end{equation}
where \(N\) is the normalization constant.
Find \(N\).
Plot this wave function.
Plot the probability density.
Find the probability that if you measured \(L_z\) you would get \(3\hbar\).
What is the expectation value of \(L_z\) in this state?